Rotation from Oscillating Axis Of Rotation

[Omikhiro]

Hello. I was considering a case where a rod could rotate about its end freely on an axle. The axle is moved back and forth linearly and periodically, causing the rod to spin.

Why is the rod spinning? Is it because after the axle has moved its distance in one direction and has stopped to move in the other direction, it is adding tangential velocity to the rod?

 

[Spinnor]

I sketch showing the motion would equal many words.

 

[TESL@]

It is applying torque with respect to the COM of the rod except two positions where the direction of oscillations align with the rod, thus the rod rotates and oscillates at the same time.